Find a unit vector w in the direction of u?

Question

Let #vec u#=#<##4/3#,-1,#2/3##>#

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Answer 1 · 2018-07-24T19:43:06

# (4/sqrt29,-3/sqrt29,2/sqrt29).#

#vecw# and #vecu# have the same direction.

#:. vecw=kvecu=k(4/3,-1,2/3)," where, "k gt 0, #

#, or, vecw=(4/3k,-k,2/3k)#.

Also, #vecw# is requred to be a unit vector.

# :. ||vecw||=1#.

#:. sqrt{(4/3k)^2+(-k)^2+(2/3k)^2}=1#.

#:. sqrt(29/9k^2)=1#.

#:. sqrt29/3|k|=1#.

#:. k=+3/sqrt29, because, k gt 0#.

#rArrvecw=(4/sqrt29,-3/sqrt29,2/sqrt29),# is the desired vector.